House Price Change and Highway Construction: Spatial and Temporal Heterogeneity (Presented at the American Real Estate Society conference, April 2008) Michael Reibel 1 , Ekaterina Chernobai 2 and Michael Carney 3
Draft: March 31, 2008
Abstract This paper studies the effect of a newly completed highway extension on home values in the surrounding area. We analyze non-linearities in both the effect of distance from the freeway and the effect of time relative to the completion of the road segment. While previous studies of the effects of nearby amenities on property and land values have focused on either cross-sectional spatial or temporal patterns, the joint analysis of the two dimensions has not been thoroughly investigated. We use home sale data from a period of four years centered around the completion of a new highway extension in metropolitan Los Angeles. We combine a standard hedonic model with a spline regression technique to allow for non-linear variations of the effect along the temporal and spatial dimensions. Our empirical results show that the maximum home price appreciation caused by the new freeway extension occurs at moderate distances from the freeway only after it is completed. Lower price increases for this period are observed for homes sold closer to the freeway or much further away. There is no statistically significant distance dependency in the two years immediately prior to the extension completion. This indicates that the housing market is not fully efficient as the information about the impending completion of the freeway is not immediately incorporated into sales prices.
Introduction The effect of nearby amenities on home prices has been an important question in urban economics since the late 1970s. At equilibrium, amenities (or disamenities) that are 1
2
3
Department of Geography and Anthropology, California State Polytechnic University, Pomona. (E-mail:
[email protected]) Department of Finance, Real Estate and Law, California State Polytechnic University, Pomona. (E-mail:
[email protected]) Department of Finance, Real Estate and Law, California State Polytechnic University, Pomona. (E-mail:
[email protected])
sufficiently close and sufficiently large as to affect homeowners’ utility will be internalized into house values. This self-evident statement, however, does not resolve which amenities have significant utility effects, the magnitude or even the direction of those effects or of course, whether the system is in fact at equilibrium (i.e. whether utility effects are fully internalized by the market pricing mechanism). More germane to our current purposes, the phrase “sufficiently close and sufficiently large” is vague; moreover there are further questions about the timing of the price changes corresponding to the market internalization of new amenities. This empirical paper investigates the spatial and temporal heterogeneity of house price responses to new highway construction using the example of the Interstate 210 extension, which opened November 2002 in Southern California. The case study is deliberately modest in its scope, allowing us to focus in depth on the issues of spatial and temporal heterogeneity in house price responses. Specifically, we focus on a single very large new amenity (a ten mile stretch of ten-lane interstate highway), in the absence of other important contemporaneous new amenities, thus effectively isolating its effect. Our focus on observed price changes obviates the theoretical question of equilibrium while imposing no assumptions about the direction or magnitude of actual price effects. Finally, we estimate our models for a regular series of distances from the new road, and time points both before and after the opening of the road, permitting us to track price effects across various distances and over time. We hypothesize that, first, the effect on home prices in the vicinity of the freeway extension would be gradual over time since homeowners generally appear to be slow to adjust home prices to changes in fundamentals. Second, we expect the price effect of the freeway extension to be nonlinear and polytonic over distance. Specifically, for homes in closest proximity to the freeway extension the negative externalities are expected to dominate the positive externalities, exerting downward pressure on the prices of those homes ceteris paribus. On the other hand, homes at moderate distance from the extension, the transportation benefits of the freeway will dominate the inconveniences caused by additional noise and air pollution resulting in higher home prices ceteris paribus. At a certain distance threshold (to be empirically determined), the price effect of the amenity is expected to fall asymptotically to zero. We also investigate how this distance decay function may be changing over time prior to and after the freeway extension completion. The need for a new east-west freeway connection between Los Angeles and San Bernardino counties was identified as early as in the middle of the 20th century. It was needed for both travelers and commuters in order to relieve the traffic congestion on other local freeways and streets between the cities of San Dimas and San Bernardino. The construction of the main portion of the proposed 28-mile freeway extension, stretching for 20 miles between San Dimas to Rialto, was started in early 1998 by the two funding and construction partners of the project, SANBAG (San Bernardino Associated
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Governments) and Caltrans (California Department of Transportation). It was completed on November 24, 2002 4 . The structure of the paper is as follows. The next section summarizes the theoretical background and reviews related literature on the effects of local amenities on prices of the surrounding properties. It is followed by the description of data and methodology utilized for this paper. The results of the empirical analysis of the data are summarized next. The last section concludes.
Theoretical Background There have been hundreds of studies using hedonic models to estimate the effect of nearby amenities on urban land and or home prices. The first works on hedonic estimation are Rosen (1974) and Griliches (1971). In this approach, the price of an individual property is modeled as a function of its physical, location and neighborhood characteristics. Early studies applying hedonic methods to home prices and urban land include Brown and Pollakowski, 1977; Goodman, 1978; Harrison and Rubinfeld, 1978; Lafferty and Frech, 1978; and Nelson, 1978. A more recent important general study on a very large Florida sample is Archer et al. (1996). Subsequent work has often attempted to isolate the effects on home prices of particular local factors of concern. Such factors include point source pollution (Brasington and Hite, 2005), school quality (Leech and Campos, 2003; Haurin and Brasington, 1996), and traffic externalities (Hughes and Sirmans, 1992). Particularly in the last few year such studies have focused on the effects on house prices of such human-scale local amenities as green space (Kong et al., 2007), bodies of water (Mahan et al., 2000; Larson and Santelmann, 2007) and pedestrian-friendliness and new urbanist design (Kahn, 2007; Matthews and Turnbull, 2007; Song and Knapp, 2003). Another interesting development in the literature on hedonic estimation of the determinants of house prices, and one with long-range theoretical relevance for studies of the effects of transportation infrastructure investments, is research on the definition of urban housing submarkets (Bourassa et al., 1999) and on the price gradients associated with the multiple cores of multinodal cities (Plaut and Plaut, 1998; Waddell et al., 1993, Dubin and Sung, 1987). Instead of seeking to use price differentials to reveal the implicit price effects of household and/or local (dis)amenities, these studies treat the details of urban morphology itself as amenities. Conceptually, they bridge the gap between hedonic modeling of amenity effects and the seminal urban land rent theories of Alonso (1964) and Muth (1969). These earlier studies were much simpler, relying as they did on a conception of urban form dominated by a single central business district core. Further developments of this sort in urban morphology may influence future studies of transport infrastructure because of their potential implications for the value of accessibility to secondary nodes in the urban system. 4
The remaining 8-mile eastern portion of the freeway extension was completed on July 24, 2007. It stretches between Rialto and San Bernardino. Information source: www.sanbag.ca.gov
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Of more immediate relevance to our analysis, many studies specifically address the marginal effects of investment in the transportation infrastructure on affected home prices. A number of these document the positive effects on home values of the addition of nearby rail stations (Benjamin and Sirmans, 1996; Gatzlaff and Smith, 1993). Debrezion et al. (2007) found a stronger positive impact of new rail station construction on commercial property values at short distances and on residential values at slightly longer distances. Gibbons and Machin (2005) employ a quasi-experimental design comparing house price appreciation for a treatment group (homes for which new stations made rail more accessible) and control group (otherwise similar nearby homes not affected by new stations). Other rail station studies include Bowes and Ihlandfeldt (2001) and McMillen and McDonald (2004). Both of these studies use a set of dummy variables to code for distance from sample homes to rail stations. Bowes and Ihlandfeldt found the most positive effects in richer, more peripheral neighborhoods, while McMillen and McDonald found a steep negative price gradient with increasing distance from new stations. Studies examining the impact of new automobile oriented infrastructure on land values are less common than studies of the impact of rail investment. Mikelbank (2004) speculates that this is because of the more generally large, discrete and separable nature of major rail infrastructure investments, which makes it easier to analyze their net effects than those of road building. Kilpatrick et al. (2007) emphasize the negative impact on house prices of nearby superhighways and tunnels when access points are more distant. Mikelbank (2004, 2005) examines the effects of smaller, more numerous road infrastructure investments in Ohio with mixed results. Smersh and Smith (2000) find construction of a new bridge impacts positively on peripheral areas that subsequently enjoy greater access but negatively on more central areas that experience greater congestion. In addition to the increasing range of causal factors examined, there has been considerable methodological refinement in the hedonic estimation of house prices. A number of studies incorporate spatial statistics or spatial interactions in the estimation of models (Mikelbank, 2004; Fik et al., 2003; Can and Megbolugbe, 1997; Can 1992). By contrast, Bourassa et al (2007) find that spatial econometrics do not improve the estimation of house prices in their sample. Dubin (1998) provides an excellent overview of the kriging technique and its applications in house price research. Case et al. (2004) contrast several spatial econometric specifications and find evidence that such models incorporating nearest neighbor information perform better than more typical local regression models. Whether or not spatial statistics are applied, many of the studies of the effects of transportation infrastructure on house prices are disaggregated by distance or otherwise designed in such a way that they reveal major non-linearities in the effects of distance from relevant new transportation amenities (Kilpatrick et al., 2007; Debrezion et al., 2007; Waddell et al., 1993). In particular, effects are often found to be negative at very short distances, because of noise, pollution, and (particularly in the case of rail stations) excessive foot traffic and possibly crime. At the next functional range of distances, the
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amenities are still close enough to be beneficial but the negative effects are diminished, resulting in a positive overall effect on house prices. At greater distances the value of the amenity gradually declines to zero. Likewise, the effects of new transport amenities are not constant over time, and the effect of the time variable is also non-linear. Several studies show effects anticipating transport amenities that have been announced and/or are under construction but are not yet available for use. Yiu and Wang (2005) found positive effects anticipating the opening of a new tunnel in Hong Kong. McMillen an McDonald (2004) found similar positive anticipation effects for the Midway rail line in Chicago. Conversely Mikelbank (2004) found negative anticipation effects. Smersh and Smith (2000) found mixed effects that were consistent both before and after the opening of the bridge in their study. Other studies probe the question of price adjustments over time following the availability of a new transportation amenity. Mikelbank (2005) shows negative effects one year after availability, near zero effects at slightly more than two years after availability, peaking at three years after, and followed by a slow decline. He speculates that the brief negative effect might be due to temporary congestion resulting from the travel adjustment process. Because these distance gradients and time lags in the effects of transportation infrastructure investment are expected to be non-linear, a particularly promising methodology for these purposes is spline regression (Bao and Wan, 2004; Smersh and Smith, 2000). Splines are essentially piecewise regression models that are constrained in such a way that there are no jumps (discontinuities) between segments, but rather changes in slope at the segment junction points (called knots). The result is a continuous estimation in which the changing slopes of the segments represent effects at successive values of the spline variable. By using spline regression models in our study we probe the non-linearities in the effects of both distance and time from the initial availability of major transportation infrastructure amenities, a freeway extension in metropolitan Los Angeles. Such nonlinearities have been demonstrated separately in previous studies but never jointly analyzed; thus, we believe that our study would make a contribution to the literature on the effects of distance from amenities on home values.
Data and methodology The empirical data for the estimations was obtained from DataQuick Information Systems and made available to the Real Estate Research Council of Southern California at California State University, Pomona. Housing data for a total of 5,566 home sales in San Dimas, La Verne, Pomona and Claremont was extracted for the period between December 1, 2000 and December 1, 2004. This covers a four-year period, two years before to two years after the freeway extension completion. The DataQuick dataset provides information only for the most recent sale of each individual house that occurred within the period. If a house was sold more than once within the period, then only the last sale will be recorded in the sample.
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The data provides information about the physical characteristics of each property which included sales price, home and lot sizes, property age, number of bedrooms and bathrooms, existence of heating and cooling systems, among others. The description of the property characteristics obtained from the dataset, as well as other control variables used in the estimations, is provided in Table 1. The descriptive statistics for them are summarized in Table 2. Value is the dollar assessed value of the house which is used as the dependent variable in the hedonic regression estimations in this study. SqftHome and SqftLot are the total areas of the house and of the lot, respectively, measured in square feet. The size of each is expected to positively affect the Value. A related variable, PercentImprove, shows the percentage of improvement on land, or the percentage of the lot used for the structure. A lower percentage is expected to contribute to a higher property value since this would indicate a higher amount of land that comes with the house. We expect that multicollinearity between the percentage of improvement and the previous two variables is not likely since the house structure may take different length and width dimensions as well as occupy two or more floors. Thus there should be no clear relationship between the size of the home, the size of the lot and the fraction of the lot that the structure occupies. The age of the house, Age, measured in years, is one of the negative factors affecting home value and we thus expect to see a negative coefficient for this independent variable. Instead of using the number of bedrooms as an independent variable we decided to use AllRooms which adds extra rooms in the house to the number of bedrooms. Our argument is that each additional room in the house is viewed by households as an added value, and in addition many extra rooms could be converted into additional bedrooms. Different regression models that were attempted for data fitting in this study showed that this variable gives statistically better results than for those in which the number of bedrooms was used instead. For a similar reason, we decided to not use the number of bathrooms directly in our models but to use the number of bedrooms less the number of bathrooms, BedLessBath. This reflects how many bedrooms come without a bathroom and is thus viewed by households as a disadvantage. For example, having not three but only two bathrooms in a house will not necessarily decrease home value if there are a total of only two bedrooms in the house; having too much space in the house allocated for bathrooms may be viewed as a space inefficiency and may thus lower the house value. Heat and Cool dummy variables reflect the presence of heating and cooling systems in the house which are expected to affect positively the value of the house. To control for market conditions, LastMonth30r and Change30r are used to indicate the level of the 30-year fixed rate mortgage rate. LastMonth30r is the daily average mortgage rate for the previous calendar month. We believe that using the recent average rate is more accurate than the one on the property sale day since homeowners selling their homes consider a recent trend in the rate at the time they put their properties for sale. Change30r is the change in LastMonth30r between the last two calendar months. This
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Table 1. Description of variables used in estimations ___________________________________________________________________________________________________________
Variable Description Units ______________________________________________________________________________ Value: SqftHome: SqftLot: Age: AllRooms: BedLessBath: Heat: Cool: LastMonth30r: Change30r: PercentImprove: Miles m2 m3 m4 m5 m6 m7 Open-i Open+i Time
Assessed value of the house Total area of the house Total area of the lot Age of house calculated by subtracting the year built from the year of sale date Total number of rooms in the house (bedrooms and extra rooms) Number of bedrooms less number of bathrooms Dummy variable: 1 if heating exists, 0 otherwise Dummy variable: 1 if cooling exists, 0 otherwise Average 30-year fixed mortgage rate for the previous calendar month Difference in the average 30-year fixed mortgage rate between two previous calendar months Percentage of the improvement on the property Distance from the freeway extension Distance from the freeway extension less 0.4 miles Distance from the freeway extension less 0.8 miles Distance from the freeway extension less 1.2 miles Distance from the freeway extension less 1.6 miles Distance from the freeway extension less 2.0 miles Distance from the freeway extension less 2.4 miles Dummy for i-th year preceding the freeway extension opening date, i = 1, 2 Dummy for i-th year following the freeway extension opening date, i = 1, 2 Number of days between 12/1/2000 and sale date of the house
dollars square feet square feet years
percent percent percent miles miles miles miles miles miles miles
days
____________________________________________________________________________________________________________
Table 2. Summary statistics of variables used in estimations (N = 2,259) Variable
Mean
St. Dev.
Minimum
Maximum
Range
Value SqftHome SqftLot Age AllRooms BedLessBath Heat Cool LastMonth30r Change30r PercentImprove Miles Time
316,070.3 1,575.22 10,359.9 44 8.31 1.25 0.99 0.24 5.15 -0.003 38.26 1.37 851.32
140,168.2 504.99 23,745.06 16 1.99 0.68 0.11 0.43 0.35 0.21 13.7 0.9 402.8
8,400 480 126 0 3 -1 0 0 4.37 -0.37 0 0 0
1,700,000 5,695 757,900 114 19 5 1 1 5.78 0.55 93 3 1,460
1,691,600 5,215 757,774 114 16 6 1 1 1.4 0.92 93 3 1,460
Note: The means for Heat and Cool indicate the percentage of homes that have heating or cooling, respectively.
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variable is expected to proxy for the expectation about the direction of the mortgage rates prevailing in the market. The data was used to estimate the change in the effect of the proximity to the freeway extension on property values over the four-year period. The distance to the freeway for each property was obtained using geo-coding techniques of geoprocessing tools in ArcGIS Geographic Information Systems (GIS) software. The distance is measured in miles and is labeled Miles in our estimations. To obtain the change over time in the effect of the distance to the freeway extension we split the dataset into four subsets – two before and two after the extension opening date – that contain data for a year-long period in each. For example, the first subset contains data for the period between December 1, 2000 and November 23, 2001. The remaining three subsets cover consecutive years with the last one being November 24, 2003 through December 1, 2004. The hedonic regressions are then run for all respective subsets simultaneously as a system. We restrict the non-varying coefficients of the independent variables, other than those controlling for the distance effects, to be the same across the individual regressions. This way only the distance effects may vary over time. While obtaining a continuous distance effect path is impossible, we believe that this regression technique becomes a good approximation of the time path of the distance effect on property values. First, we run a “global” hedonic linear regression model over the entire dataset covering the four-year period: “Global” model: Value = f (const, SqftHome, SqftHome2, SqftLot, SqftLot2, Age, Age2, AllRooms, AllRooms2, BedLessBath, BedLessBath2, Heat, Cool, PercentImprove, PercentImprove2, LastMonth30r, Change30r, Open -2 , Open +1 , Open +2 ) This regression model includes the physical characteristics and the market conditions variables described earlier. It also contains dummy variables that control for the year of sale. The dummies are denoted by Open -i and Open +i and represent i-th year preceding or following the freeway extension opening date, respectively, where i = 1, 2. The squared values in the constructed model are expected to detect the presence of convexities in the effect of the variables on the property value. Next, we remove the time dummies from the “global” regression model and fit the resulting “local” model to the data in each of the subsets in a system, as was explained earlier. We use three forms of the “local” model. In “local” model (a), no distance variable is included. Thus, it ignores any potential effect of the distance from the freeway extension on property value completely. A “local” model (b) includes all independent variables that model (a) contains and an additional Miles variable which will detect the linear relationship between the proximity to the freeway extension and the property value. The further from the freeway the lower
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the home value is expected to get due to the inconvenience caused by longer time required to drive to the freeway. Thus we expect to see a negative regression coefficient. A “local” model (c) includes all independent variables that model (b) does plus additional distance spline variables that will detect any nonlinearities in the dependence of the property values on their distance away from the freeway extension. For consistency between the data subsets, we fixed the distance cutoffs used for the spline knots in each subset. The cutoffs are in 0.4 mile increments: 0.4 miles, 0.8 miles, 1.2 miles, 1.6 miles, 2.0 miles and 2.4 miles away from the freeway. 0.4 mile distance increments appear to be optimal. Larger increments appeared to be not good enough to catch short distance nonlinearities especially for homes lying in relatively close proximity to the freeway. On the other hand, smaller increments weaken the regression results by making the number of observations between any two adjacent distance cutoffs too small. Following the spline technique methodology of Marsh and Cormier (2001) we construct the spline adjustment variables in “local” regression model (c) in the following way. The six distance cutoffs explained earlier require us to first create six dummy variables D 1M , D 2M , D 3M , D 4M , D 5M , and D 6M . Here, D 1M = 1 when the distance to the freeway is more than the first distance cutoff of 0.4 miles, and D 1M = 0 when the distance is less than 0.4 miles. Similarly, D 2M = 1 when the distance to the freeway is more than the second distance cutoff of 0.8 miles, and D 2M = 0 when the distance is less than 0.8 miles, and so on. These dummy variables are then used to construct the spline adjustment variables m2, m3, m4, m5, m6, m7, corresponding to the second, third, fourth, fifth, sixth and seventh 0.4 mile distance segments, respectively. Here, m2 = D 1M (Miles – 0.4), m3 = D 2M (Miles – 0.8), and so on. The coefficients of these six spline adjustment variables thus indicate the additional effects of the distance on home value relative to that in the distance segment next closest to the freeway. For example, to determine the effect of the distance on home value for homes located 0.8 to 1.2 miles away from the freeway extension, one needs to sum the regression coefficients for Miles, m2 and m3 spline regression variables. In summary, the three “local” regression models are: “Local” model (a): “Local” model (b): “Local” model (c):
“Global” model without the time dummy variables “Local” model (a) with the additional variable Miles “Local” model (b) with the additional distance spline adjustment variables m2, m3, m4, m5, m6, m7
Our hypothesis is that, first, there may be statistically significant non-linear effects of the distance on sales values of the properties. This should get reflected in a better fit of the regression model with the distance spline variables producing an R-squared higher in “local” model (c) than in “local” models (a) and (b). Second, we hypothesize that the spline variable coefficients will indicate an initial increase in the total distance effect
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followed by a decrease as homes get more distant from the freeway extension. We believe this effect would become more noticeable for later time periods of the dataset as households take time to readjust their home prices in response to the changes in the local amenities. For an additional testing of our hypothesis of a time-varying effect of the distance from the freeway extension on property values, we split the entire data set into seven subsets. Each contains homes lying in different distance intervals on both sides of the freeway extension. For example, in the first subset we only left those homes that lie within 0.4 miles away from the extension, the second subset contains homes that lie 0.4 to 0.8 miles away from the extension, and so on. Since we no longer need to control for the distance in each subset, using the same system estimation technique we run for each subset a “local” model (a) that also contains two additional variables. The first variable Time shows the number of days between December 1, 2000 and the sale date of the house. The second variable Complete is a time spline adjustment variable created following the same method that was used to create the distance spline adjustment variables explained earlier. It shows the number of days between the freeway extension completion date, November 24, 2002, and sale date if house was sold after this date, and 0 otherwise. The results of these additional regressions are expected to show whether there existed any differences in the speed of home value increases over the four-year period for homes sold in different distance rings on both sides of the freeway extension. We expect to see the slowest increase in value for properties in the closest and longest proximity to the freeway, and the fastest increase in value for properties at moderate distances from the freeway.
Results Elimination of observations with missing value variables left 2,262 out of the original 2,575 observations for homes sold within the four-year period and located within 3 miles from the freeway extension. The regression results for the “global” model with year dummies are summarized in Table 1. About 67 percent of the variations in home values are explained by the variations in the chosen independent variables as is indicated by the R2. The majority of the independent variables are statistically significant at the 1 percent level, and some other are significant at 5 or 10 percent. As expected, both SqftHome and SqftLot positively affect home value although the absolute magnitude of the effect appears to be rather small. When the size of the house is measured in the number of rooms the magnitude of the effect on home value appears much larger with an additional room in the house raising the value by $29,050. Each bedroom that comes without a bathroom decreases the value of the house by $16,680. As was discussed in the earlier section, this supports our suggested argument that the advantage of having an extra bedroom is weakened if the house does not provide
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an additional bathroom. The significance of the coefficients for the squared variables suggests the presence of strong convexities or concavities in the effects. The percentage of improvement on land, PercentImprove, statistically significantly raises the property value by about $6,963 per each percentage point with a slight concavity in the effect. Age decreases home value with the marginal coefficient equal to $2,623. The significance of the coefficient for Age2 indicates the weakening of the effect as the house becomes much older. The presence of cooling in the house raises house value by almost $34,346. The effect of Heat is also positive although not statistically significant. A percent increase in the 30-year fixed mortgage rates increases home values by $17,705. The positive statistically significant coefficients for the dummy variables used to control for the year of sale confirm that over the four years home prices have been increasing. Moreover, they have been doing so at an increasing rate as can be seen from the increasing differences between the year dummy coefficients. The same “global” model, excluding the dummy variables, was used to fit the data in the system consisting of the four one-year subsets. As was explained in the earlier section, we include additional variables that control for the distance of each house from the 210 freeway extension. The linear effect of the distance on home values in each subset is measured in a “local” regression model (b), and the non-linear effect in a “local” model (c). Model (a) does not control for the distance. The regression results for the three “local” models for each subset are shown in Table 2. As the coefficients for the majority of the independent variables remain statistically significant at least at the 10 percent level, the table only presents the results for the goodness-of-fit and the distance variable coefficients. Those for the “global” model, with and without the distance variables, are also included in the table for comparison. First, the results in Table 2 indicate that for the entire dataset and for the four subsets the goodness-of-fit of the hedonic regression model increases when property values are controlled for the distance from the 210 freeway extension. In each case the value of R2 is higher in model (b), which contains the linear distance variable, Miles, relative to model (a). The expected negative sign of the Miles coefficient and the 1 percent significance level in all but the first year of the four-year period of interest suggest that the further from the freeway the lower the house value. Based on our regression models, an additional mile away from the freeway decreases home value by $18,276, $23,119, and $29,962, for the year preceding and the two years following the freeway completion, respectively. The negative distance effect thus gets stronger over time. Second, regression model (c) results indicate that for all subsets the model fits the data at least as well when one controls for non-linear effects of the distance using the spline technique described in the earlier section. The distance spline variable coefficients reflecting marginal effects of the distance on property values appear to be statistically significant for close distances to the 210 freeway extension after the extension was completed. The fact that the effects of distance on home values do not appear significant before the freeway completion may imply that households were slow to change their
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Table 1. Hedonic regression results for the “global” model with year dummies.
Variable
Coefficient
t-statistic
Constant
-179,578.4
-3.2325
SqftHome
28.0263
1.6362
SqftHome2
0.0284
7.0634
***
SqftLot
3.9098
14.7414
***
SqftLot2
-0.0001
-14.2357
***
Age
-2,622.735
-5.0429
***
29.8186
6.8126
***
29,049.66
4.8527
***
AllRooms
-1,421.071
-4.3854
***
BedLessBath
-16,680
-2.7668
***
BedLessBath2
3,351.763
1.6918
*
Heat
11,211.55
0.7485
Cool
34,345.59
6.5249
***
6,963.42
12.7474
***
PercentImprove
-113.0195
-19.3086
***
LastMonth30r
17,705.4
2.1433
**
Change30r
-7,218.281
-0.768
Open -1
30,309.89
4.988
***
Open +1
69,902.07
8.9312
***
Open +2
136.434.5
20.3681
***
2
Age
AllRooms 2
PercentImprove 2
R
2
0.6736
Number of observations = 2,262 The dependent variable is Value. * indicates 10 percent statistical significance ** indicates 5 percent statistical significance *** indicates 1 percent statistical significance
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***
Table 2. Results of hedonic regression models (a), (b), and (c) for full dataset and four one-year subsets.
Full dataset
One-year subsets Open -2
Open -1
Open +1
Open +2
2,262 obs.
381 obs.
381 obs.
760 obs.
740 obs.
(a) R2
0.691
0.325
0.582
0.656
0.656
(b) R2
0.706
0.373
0.612
0.674
0.672
-18,276.45 ***
-23,118.78 ***
-29,961.71 ***
0.618
0.685
0.678
95,630.61 **
101,976.3 **
-142,657.7 *
-129,130.3 *
Miles 2
(c) R
-21,980 *** 0.711
0.373
Miles m2 m3 m4 m5 m6 m7 NOTES:
Regression models (a), (b), and (c) for the full sample include year dummy variables. The dependent variable in each hedonic regression model is Value. Model (a) contains no distance variables. Model (b) contains linear distance variable, Miles. Model (c) contains distance spline variables. * indicates 10 percent statistical significance. ** indicates 5 percent statistical significance. *** indicates 1 percent statistical significance. Distance spline variable coefficients not statistically significant at the above levels were omitted.
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pricing in response to the change in surrounding amenities despite the fact that the information about the new freeway extension under construction was already publicly available. In our econometric model this may also be due to a smaller sample size for the earlier subsets of data making them not large enough to detect the distance effects on home values. The marginal distance effects for the two years following the freeway opening can be converted into total effects of the distance on home values for each 0.4 mile distance segment. For example, within 0.4 miles from the freeway the value of homes that were sold within one year from the freeway completion rises by $95,631 per each mile as the distance from the freeway rises, as indicated in Table 2. For the second 0.4 mile distance segment in that time period home prices fall by $47,027 per each mile – this number comes from taking the sum of Miles and m2 coefficients 95,631 and -142,658, respectively. The results for the two-year period, when split into two year-long periods, are summarized in Table 3. From the resulting total distance effects one can also infer the difference in home values between the beginning and the end of 0.4 mile segments, summarized in the table in the last column for each time period. The numbers in Table 3 support our hypothesis that there exist non-linearities in the effects of the distance to the freeway on property values. According to our hypothesis, home values should first increase and then gradually decrease as the distance rises. We also hypothesized that these distance effects would not be immediately incorporated in home values when the information regarding the freeway construction was already publicly available, thus creating a delay in the occurrence of the effects. Table 3 shows that homes that were sold in the first year after the extension was completed and that lie 0.4 miles from the freeway are $38,252 more expensive than homes sold right next to the freeway, when physical characteristics are controlled for. According to our hypothesis, this may reflect the presence of negative externalities caused by the noise generated by the freeway traffic. The corresponding number for homes sold in the second year is slightly higher at $40,790. The price of homes sold 0.8 miles from the freeway is $18,811 and $10,862 lower than for those that lie 0.4 miles from the freeway for the two respective years. This may reflect the increasing disadvantage of being located further away from the freeway. Table 4 summarizes the results of the hedonic regressions performed in a system for the seven 0.4 mile distance subsets and aimed at identifying any differences in the time path of the house value appreciation. The first system of regressions does not control for the time when a house was sold. The second one contains the Time variable and identifies the linear effect of time, measured in days, on the house value. The third model is expected to produce a more accurate time trend as it contains an additional time spline variable Complete. This model aims at identifying additional differences in the time effects following the freeway extension completion date, November 24, 2002. The inclusion of variables that control for the time of sale improve the goodness-of-fit of the hedonic regression model as is indicated by the higher R2 for model (a) with Time variable, and an even higher R2 for model (a) with time spline variables. This is true for
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Table 3.
Non-linear effects of the distance to the freeway extension on home values.
0~0.4 miles 0.4-0.8 miles
Table 4.
Homes sold within the 1st year following freeway completion
Homes sold within the 2nd year following freeway completion
Marginal effect, $ per mile
Total effect, $ per mile
Price change over 0.4 miles, $
Marginal effect, $ per mile
Total effect, $ per mile
Price change over 0.4 miles, $
95,631 -142,658
95,631 -47,027
38,252 -18,811
101,976 -129,130
101,976 -27,154
40,790 -10,862
Results of hedonic regressions with and without time variables for full dataset and seven distance subsets.
Full Distance subsets dataset 0-0.4 0.4-0.8 0.8-1.2 1.2-1.6 1.6-2.0 2.0-2.4 miles miles miles miles miles miles
2.4-3.0 miles
2,262 obs.
391 obs.
369 obs.
348 obs.
317 obs.
134 obs.
259 obs.
444 obs.
R2
0.585
0.415
0.577
0.55
0.527
0.725
0.620
0.575
(a) with R2 Time
0.684
0.603
0.725
0.661
0.613
0.809
0.700
0.690
140 ***
164 ***
149 ***
172 ***
140 ***
145 ***
109 ***
123 ***
0.690
0.608
0.734
0.668
0.617
0.812
0.706
0.711
54 *** 137 ***
86 *** 126 ***
61 ** 146 ***
78 *** 154 ***
62 ** 119 ***
79 **
54 * 80 *
179 ***
(a)
Time
(a) with R2 time spline Time Complete NOTES:
Regression model (a) for the full sample is the “global” model that excludes time period dummy variables. The dependent variable in each hedonic regression model is Value. * indicates 10 percent statistical significance. ** indicates 5 percent statistical significance. *** indicates 1 percent statistical significance. Time spline variable coefficients not statistically significant at the above levels were omitted.
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all seven distance subsets as well as for the entire dataset. In the “local” models that show a linear relationship between sale time and home value the Time coefficients indicate an increase in home prices at the speed of $109 to $172 per day depending on the subset, and they are all statistically significant at 1 percent level. For all distance subsets the results of the hedonic model containing time spline variables indicate a faster increase in house values following the freeway extension opening date. The regression coefficients for the variable Complete indicate that the price appreciation, caused by the freeway extension opening, is slow in the closest proximity to the freeway (within 0.4 miles), faster in the next two distance intervals, followed by slower appreciations at the subsequent distances. Interestingly, the price appreciation is even faster at the highest distance from the 210 freeway extension (the coefficient of 179) – this can potentially be explained by the relieved traffic congestion in the area of the former only east-west Interstate highway (FWY10), which lies about 3 miles south from Interstate 210, causing local home prices in that region to rise faster. These differences in the time paths of home value appreciation for the later two years of our sample produce a pattern of non-linear effects on home values of the distance from the freeway. In particular, the additional speed of price appreciation following the extension opening is the slowest for homes in the closest proximity to the freeway (within 0.4 miles), a lot faster at moderate distances, and slower again as the distance further increases. This produced pattern is consistent with that obtained from the systems of regressions for different time periods presented earlier.
Discussion The object of our study has been to use spline regression models to probe the nonlinearities in the effects of both distance and time from the initial availability of major transportation infrastructure amenities – in our case, a freeway extension in metropolitan Los Angeles. Such non-linearities have been demonstrated separately in previous studies but never jointly analyzed as is done in our empirical case study. In our incremental approach, we first modeled a standard hedonic regression of house prices on housing characteristics and contextual variables including dummy variables for year of sale (to control for the global effect of a rapidly appreciating metropolitan housing market). These results are consistent with those from many earlier studies in the same vein. Our next step was to disaggregate data along the time dimension and analyze them separately for two years before and two years after the opening of the freeway extension. For each of the four years we estimated separate models without any variable capturing distance to the freeway extension, then with linear distance, and finally with distance splines. The linear distance model shows the expected consistent decline with increasing distance from the freeway extension. When the spline model for distance ranges is fitted we find no statistically significant distance effect anticipating the freeway opening, and the expected pattern of positive effects at shorter distances followed by mildly negative effects at moderate distances. The latter is interpreted as reflecting a decline in the
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competitive advantage of these properties relative to those closer to the freeway extension. At longer distances, as expected, the effects fade into insignificance. Our final step was to reverse the relationship of time and distance in our models. In other words, we disaggregated the sample by 0.4 mile distance intervals and modeled the effects of time. Once again, time effects were modeled first as continuous and linear and subsequently as a spline. The time analysis reflects the distance effects already discussed; in other words, after the freeway extension completion homes at the closest and more distant regions appreciated less rapidly than homes in the intermediate distance intervals. More generally, our analysis adds to a growing literature on the use of splines to examine specific time and distance non-linearities in the effects of local amenities on house prices. We maintain that while spatial regression models may be a beneficial refinement of standard hedonic price models of housing amenities they do not provide concrete information on the form of time and distance decay functions. Splines, on the other hand, serve this purpose.
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